The two channels of the power supply are not internally connected. They are floating with respect to each other. If you wanted to, you could connect them in series (negative of ch 2 to positive of ch 1 or vice-versa) to get higher voltage. There is no restriction of how you connect the two of them. Think of them like two separate adjustable batteries. Also note that both channels are floating with respect to earth/ground. You may (if you choose to) connect any reasonable point in your circuit to one of the ground terminals of the power supply, to provide a ground reference, but this is not strictly necessary. In fact, if you are going to use an oscilloscope to probe signals in the circuit, you usually want to leave the circuit floating, to prevent ground loops (through the additional ground connection of the scope probe).
That said, you must connect both the positive and negative terminal of each channel to something in your circuit. From your description it sounds like you did not connect the negative/black side of channel 1 (12 V) power supply. In the basic Dave's DC load, the circuit's op-amps power and the input (load) power are both connected to a common circuit "ground" (not to be confused with real "earth" ground, a circuit "ground" is just the "zero volt" reference for the circuit... it is not necessarily connected to a real earth/ground). So the circuit worked when you connected both negative terminals together at the breadboard.
Speaking of breadboards, be careful how much current you put through it. You can and should do the high current connections (the MOSFET and current sense resistor) off the breadboard.